I think you have to keep bringing your thoughts back to you breathing, to "current" things when you're being mindful, especially if your head is doing a number on you :-) So, when you wander off and follow your story, I don't think you're being mindful at all, you're thinking about "something else" besides what's immediately in front of you, now.

I got into a long discussion with a therapist about that. I think I'm like you? If you imagine you are watching an assembly line, does the line move or do you :-) If you are moving along the line, "following the story" then you are not "letting go" of what comes in front of you and just moving "your eyes" on to the next item in front of you, letting the line do the work. The story is supposed to move, "you" are not. Don't know if that helps you any, that's the way I picture it.